Chrome Users: Please note that LastPass has problems in iOS/iPadOS and as of 13.3.1, the fault is still present. All is not lost however as LastPass in the below example is tested and known to work correctly with Firefox as of iOS/iPadOS 13.3.1.

iOS/iPadOS Settings

1. Open Settings
2. Choose Passwords & Accounts
3. Select AutoFill Passwords
4. Check the box next to LastPass
5. Uncheck the box next to iCloud Keychain.

LastPass App

Before you can access any passwords, you must have the LasstPass app installed on your iPhone/iPad and be logged-into the App with your LastPass Master Password

Web Browser

Although this example uses Firefox, the process is almost the same for Chrome users.

Step 1

1. Select the password field.
2. Open the share dialog by tapping on the 3 dots (Chrome users tap the share icon).
3. Choose "Share Page With..." I did say the process was counter-intuitive...

Step 2

Tap LastPass

Step 3

Tap the password offered in the LastPass dialog.

That's it.

Conclusion

Although not a very intuitive process, using LastPass with a browser on iOS/iPadOS it's still pretty easy to use.

Mixing with iCloud Keychain causes a lot of consistency issues for me at least.

Why are you mixing it now?

I haven't looked in awhile, but they've pretty much always had a Safari plugin. (the annoying part was that in order for it to work, you have to have the LastPass binary app installed and running, a limitation/requirement set by Apple)

EDIT: Just confirmed, Safari plugin working just fine for me. I don't use iCloud keychain generally. (mainly because it's disabled for us at work, and I like having a consistent experience as I hop between machines)